Three women, Elyse, Min and Victoria went on a shopping spree. 70% of Elyse's spending was equal to ¹₆ of Min's spending. Victoria's spending was  50% more than Min's. If Min spent another $693, she would spend the same amount of money as Victoria.

1. Find the ratio of Elyse's spending to Min's to Victoria's.
2. How much did Elyse spend?

Elyse	Min	Victoria
5x2	21x2
	2x21	3x21
10 u	42 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Elyse's spending is equal to ¹₆ of Min's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Elyse's spending = 16 of Min's spending
710 of Elyse's spending =1x76x7 of Min's spending
710 of Elyse's spending = 742 of Min's spending

Elyse : Min
10 : 42
5 : 21

Victoria's spending in percent when compared to Min's
= 100% + 50%
= 150%

Min : Victoria
100 : 150
2 : 3

Min's spending is the repeated identity.  Make Min's spending the same.  LCM of 21 and 2 is 42.

Elyse : Min : Victoria
10 : 42 : 63

(b)

	Elyse	Min	Victoria
Before	10 u	42 u	63 u
Change		+ 21 u
After	10 u	63 u	63 u

Additional amount that Min would have to spend to be the same as Victoria
= 63 u - 42 u
= 21 u

21 u = 693

1 u = 693 ÷ 21 = 33

Amount that Elyse spent
= 10 u
= 10 x 33
= $330 

Answer(s): (a) 10 : 42 : 63; (b) $330